Hubble expansion is not a velocity

Abstract

In this paper, we clarify the difference between the Hubble expansion and the Doppler shift pedagogically and illustrate both physically and mathematically why the Hubble expansion cannot be regarded as a velocity. Therefore, we suggest to replace the misleading word ‘recession velocity’ to be ‘Hubble recession’ to describe the cosmic expansion. We further derive how the peculiar velocity of a galaxy is related to its observed redshift and proper distance, which has practical use in the galaxy redshift and distance surveys.